The numerical range of banded biperiodic Toeplitz operators

The numerical range of an operator is a well studied concept with many applications in several areas of mathematics. In this paper, the numerical range of banded biperiodic Toeplitz operators is investigated, performing a reduction to the 2×2 case. Namely, the parametric equations of the boundary generating curves are deduced and two algorithms for the numerical generation of the numerical range are presented.